Question

laboratory manual math class 10 activity 16​

Answer 1

Step-by-step explanation:

sheet of white paper

A piece of cardboard

A sheet of tracing paper

A geometry box

A tube of glue

Theorem

The theorem to be verified is the converse of the theorem verified in Activity 15.

The theorem can be proved as below.

Consider a circle with radius r and centre O having two chords AB and PQ such that ∠AOB = ∠POQ (see Figure 16.1).

Math Labs with Activity - Angles Subtended by Two Chords 1

In ΔAOB and POQ, we have

AO = OP (each equal to r)

BO = OQ (each equal to r)

∠AOB = ∠POQ (given)

Then, ΔAOB is congruent to ΔPOQ (by SSA-criterion).

∴ AB = PQ.

Procedure

Step 1: Paste the sheet of white paper on the cardboard and mark a point O on this paper. With O as centre, draw a circle with any radius.

Step 2: Draw two equal angles at the centre O of the circle.

(This may be done using a pair of compasses as you have already learnt in the lower classes). Let these two angles be subtended by arcs Fig. 16.2.

AB and PQ as shown in Figure 16.2. Join AB and PQ.

Math Labs with Activity - Angles Subtended by Two Chords 2

Step 3: Trace the ΔAOB on the tracing paper.

Step 4: Place the ΔAOB obtained on the tracing paper over the ΔPOQ such that ∠AOB is superimposed over ∠POQ.

Observations

We observe that ΔAOB completely overlaps ΔPOQ. Therefore, ΔAOB is congruent to ΔPOQ.

So, we conclude that the chord AB is equal to the chord PQ.

Result

It is verified that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal.

Math Labs with ActivityMath LabsScience Practical SkillsScience Labs